Open Access
December 2018 How often does the best team win? A unified approach to understanding randomness in North American sport
Michael J. Lopez, Gregory J. Matthews, Benjamin S. Baumer
Ann. Appl. Stat. 12(4): 2483-2516 (December 2018). DOI: 10.1214/18-AOAS1165


Statistical applications in sports have long centered on how to best separate signal (e.g., team talent) from random noise. However, most of this work has concentrated on a single sport, and the development of meaningful cross-sport comparisons has been impeded by the difficulty of translating luck from one sport to another. In this manuscript we develop Bayesian state-space models using betting market data that can be uniformly applied across sporting organizations to better understand the role of randomness in game outcomes. These models can be used to extract estimates of team strength, the between-season, within-season and game-to-game variability of team strengths, as well each team’s home advantage. We implement our approach across a decade of play in each of the National Football League (NFL), National Hockey League (NHL), National Basketball Association (NBA) and Major League Baseball (MLB), finding that the NBA demonstrates both the largest dispersion in talent and the largest home advantage, while the NHL and MLB stand out for their relative randomness in game outcomes. We conclude by proposing new metrics for judging competitiveness across sports leagues, both within the regular season and using traditional postseason tournament formats. Although we focus on sports, we discuss a number of other situations in which our generalizable models might be usefully applied.


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Michael J. Lopez. Gregory J. Matthews. Benjamin S. Baumer. "How often does the best team win? A unified approach to understanding randomness in North American sport." Ann. Appl. Stat. 12 (4) 2483 - 2516, December 2018.


Received: 1 June 2017; Revised: 1 February 2018; Published: December 2018
First available in Project Euclid: 13 November 2018

zbMATH: 07029463
MathSciNet: MR3875709
Digital Object Identifier: 10.1214/18-AOAS1165

Keywords: Bayesian modeling , competitive balance , MCMC , Sports analytics

Rights: Copyright © 2018 Institute of Mathematical Statistics

Vol.12 • No. 4 • December 2018
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